Fisher information universally identifies quantum resources

Abstract

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states with and without a given resource. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states. We provide bounds on the extent of this advantage, as well as a simple criterion to test whether different resources are useful for the estimation of unitarily encoded parameters. Finally, we extend the results to show that the Fisher information is also able to identify the dynamical resourcefulness of quantum operations.